O monitoramento de vibração de máquinas rotativas é de grande interesse da indústria, uma vez que se tem a possibilidade de detectar, com certa antecedência, problemas relacionados à condição de funcionamento do equipamento, possibilitando reparos, ajustes ou consertos e, assim, minimizando custos no caso de falhas graves ou paradas inesperadas. Neste trabalho é feita a adequação de uma bancada de testes para estudo de técnicas de detecção de falhas em rolamentos de esferas por análise de vibração. O objetivo é o de localizar falhas em rolamentos utilizando o monitoramento dos sinais das vibrações (aceleração) no mancal que suporta o rolamento de teste e o posterior processamento com o auxílio de alguma técnica de detecção. Neste trabalho a técnica do envelope foi escolhida. A bancada, assim desenvolvida, permite a retirada e colocação dos rolamentos em estudo de maneira simples e rápida, permitindo a execução de diversos testes com rapidez. A investigação da detecção de falhas em rolamentos é feita comparando-se rolamentos em condições normais com rolamentos que têm um defeito induzido. Inicialmente é apresentada a descrição das origens e formas de propagação das falhas em elementos de rolamentos e também as formas como estas falhas são induzidas em locais específicos de cada rolamento. Uma breve revisão sobre métodos de detecção de falhas no domínio do tempo e da frequência é feita. Ênfase é dada ao método do envelope que faz uso da transformada de Hilbert (Hilbert Transform) conjuntamente com a transformada Rápida de Fourier (Fast Fourier Transform). Em seguida, descreve-se como foram geradas as falhas e separados os grupos de teste, também é descrito como os ensaios foram executados com os danos induzidos em local pré-determinado no rolamento. Os resultados obtidos possibilitaram identificar as origens das falhas induzidas tanto na pista externa quanto na interna dos rolamentos analisando os sinais de vibração do mancal onde está montado o rolamento em teste com o pós-processamento dos mesmos com a técnica investigada. Os testes simulam as condições extremas encontradas em sistemas rotativos de equipamentos industriais através da imposição de cargas verticais ao rolamento. Este estudo de detecção das falhas em rolamentos propiciou uma melhor compreensão e análise do processo de falha nestes componentes. / The vibration monitoring of rotating machines is of great interest to industries since it has the ability to detect, in advance, problems related to the operational condition of the equipment, enabling fixing, adjustments or repair, and thus, minimizing the cost in case of faults or unexpected downtime. In this work, the study of the adequacy of a test bench for detecting faults in ball bearings by vibration analysis techniques is developed. It aims at locating faults in ball bearings using vibration monitoring signals (acceleration) in the journal bearings that support this elements and further processing with the aid of some detection technique. In this work the envelope technique was chosen. The developed test bench thus allows the removal and placement of the bearings in a simple and fast way allowing running quickly several tests. The investigation of detecting faults in ball bearings is made by comparing the bearings under normal conditions with bearings which have an induced defect. First of all is presented a description of the origins and forms of propagation of faults in bearing elements and also the ways in which these failures are induced in specific locations of each bearing. A brief review of methods for detecting faults in the time and frequency domain is made. Emphasis is given to the Envelope Method which uses the Hilbert Transform with the Fast Fourier Transform. Then it is described how the tests were accomplished with the induced damage in predetermined sites in the bearing. The results obtained allowed to identify the origins of the induced bearing failures in both outer and inner races just by reading the vibration signals and post-processing them with the investigated technique. The tests take care to simulate conditions close to those found in actual rotatory systems of industrial equipment by imposing vertical loads to the bearing. This study in detecting flaws in balls bearings provided a better understanding of the analysis failure process in these components.

In this paper, a new concept for ultrasonic indoor positioning based on instantaneous frequency of ultrasonic signals is presented. Nonlinear phase characteristics of ultrasonic transducers introduce a frequency deviation in ultrasonic signals. By sweeping at very fast rates, a large spike in the deviation is introduced. The artefacts observable in instantaneous frequency estimations are highly localized and present an opportunity for accurate frequency detection. In order to be useful, the artefacts need to take place within the pulse and have sufficient magnitude for accurate processing. The system consists of a transducer transmitter and receiver pair, which have a center frequency of 40kHz and a bandwidth of 460Hz. In order to incorporate more transmitters, a time-division multiple access (TDMA) scheme is applied to ensure orthogonality of signals. The concept includes four ultrasonic transmitters and a single receiver, which can uniquely identify each transmitter by a distinct signal sweep. Linear chirp signals are used to form narrow pulses and ensure no interference in the TDMA scheme. The received signal is amplified and passed through a phase-locked loop (PLL) to detect the chirp signals. Accurate instantaneous frequency detection can be done on the voltage-controlled oscillator (VCO) of the PLL, which has a narrower bandwidth than the overall signal sweep. The instantaneous frequency estimation methods are largely explored in this work and consider two methods: the Hilbert transform and a zero-crossings method. This work highlights some of the advantages and disadvantages of both methods. Time of flight (ToF) in this system can ultimately be obtained by considering the instantaneous frequency estimations and the time for one particular frequency to be transmitted and received.

No description available.

In the present dissertation, we characterize the range of the attenuated Radon transform of zero, one, and two tensor fields, supported in strictly convex set. The approach is based on a Hilbert transform associated with A-analytic functions of A. Bukhgeim. We first present new necessary and sufficient conditions for a function to be in the range of the attenuated Radon transform of a sufficiently smooth function supported in the convex set. The approach is based on an explicit Hilbert transform associated with traces of the boundary of A-analytic functions in the sense of A. Bukhgeim. We then uses the range characterization of the Radon transform of functions to characterize the range of the attenuated Radon transform of vector fields as they appear in the medical diagnostic techniques of Doppler tomography. As an application we determine necessary and sufficient conditions for the Doppler and X-ray data to be mistaken for each other. We also characterize the range of real symmetric second order tensor field using the range characterization of the Radon transform of zero tensor field.

No description available.

<p>Multi-linear operators play an important role in analysis due to their multiple connections with and applications to other mathematical areas such as ergodic theory, elliptic regularity, and other problems in partial differential equations.</p> <p>Within the area of multi-linear operators, powerful methods were developed originating from the problem of the almost everywhere convergence of Fourier series. Indeed, in their work, Carleson and Fefferman lay the foundation of time-frequency analysis. By further refining their methods, M. Lacey and C. Thiele proved the boundedness of the classical bilinear Hilbert transform for a suitable range of Hölder indices.</p> <p>In this thesis, we consider the general boundedness properties of the bilinear Hilbert transform and the sub-bilinear maximal function along a suitable family of curves.</p> <p>In the first part of our work, we present a short proof of the maximal boundedness range for the sub-bilinear maximal function along non-flat curves, giving a unified treatment of both the singular and the maximal operators.</p> <p>In the second part, we discuss the boundedness of these operators along hybrid curves. This work aims to present a unified perspective that treats the case obtained by joining the zero-curvature features of the operators along flat curves with the non-zero curvature features along non-flat curves.</p>

Esta dissertação tem como objetivo principal realizar uma investigação sobre técnicas de identificação e caracterização de não linearidades em dinâmica estrutural. Em particular, busca-se aplicar as transformadas de Hilbert e Hilbert-Huang na identificação e caracterização de um sistema estrutural composto de uma viga metálica em balanço com uma massa concentrada em sua extremidade livre e apresentando uma não linearidade cúbica. Este efeito não linear é obtido através de um fio metálico tracionado que é fixo à extremidade livre da viga em balanço. O sistema é modelado através de ferramentas analíticas convencionais e o modelo do sistema é usado em simulações numéricas. Ensaios experimentais de vibração livre são realizados e os sinais medidos são usados como dados de entradas nas transformadas afim de se investigar o fenômeno não linear presente na estrutura. Os resultados simulados numéricamente apresentaram uma excelente correlação com os resultados experimentais no que se refere à identificação e caracterização do efeito não linear cubico presente no sistema. Algumas distorções entre resultados simulados e experimentais foram observados no que se refere à quantificação do parâmetro não linear, mas de forma geral, as técnicas empregadas produziram resultados bastante satisfatórios. / The major goal of this dissertation is to investigate currently available techniques to the identification and characterization of nonlinearities in structural dynamics. Particular attention is paid to the application of the Hilbert and Hilbert-Huang transforms in the nonlinearity identification and characterization process. For that purpose, a structural system composed of a steel cantilever beam carrying a lumped mass at its free end is used. The nonlinear effect is introduced by attaching the lumped mass to a thin steel wire that is positioned transversely to the beam\'s longitudinal axis. By varying the traction force on this wire different levels of nonlinearity can be observed on the beam\'s bending motion when it undergoes free vibrations. The system analytical model is obtained by employing standard modeling techniques and this model is used in numerical simulations. An experimental survey is carried out on an actual prototype in order to provide a comparison basis for the numerically simulated results. The output vibration signals resulting from either the numerical simulations and experimental tests are then used with the transform methods studied and the results are compared. A good correlation is observed between numerical and experimental data, what is a clear indication of the robustness of the Hilbert and Hilbert-Huang transforms.

Microwave signal processing in the optical domain is investigated in this thesis. Two signal processors including an all-optical fractional Hilbert transformer and an all-optical microwave differentiator are investigated and experimentally demonstrated. Specifically, the photonic-assisted fractional Hilbert transformer with tunable fractional order is implemented based on a temporal pulse shaping system incorporating a phase modulator. By applying a step function to the phase modulator to introduce a phase jump, a real-time fractional Hilbert transformer with a tunable fractional order is achieved. The microwave bandpass differentiator is implemented based on a finite impulse response (FIR) photonic microwave delay-line filter with nonuniformly-spaced taps. A microwave bandpass differentiator based on a six-tap nonuniformly-spaced photonic microwave delay-line filter with all- positive coefficients is designed, simulated, and experimentally demonstrated. The reconfigurability of the microwave bandpass differentiator is experimentally investigated. The employment of the differentiator to perform differentiation of a bandpass microwave signal is also experimentally demonstrated.

Microwave signal processing in the optical domain is investigated in this thesis. Two signal processors including an all-optical fractional Hilbert transformer and an all-optical microwave differentiator are investigated and experimentally demonstrated. Specifically, the photonic-assisted fractional Hilbert transformer with tunable fractional order is implemented based on a temporal pulse shaping system incorporating a phase modulator. By applying a step function to the phase modulator to introduce a phase jump, a real-time fractional Hilbert transformer with a tunable fractional order is achieved. The microwave bandpass differentiator is implemented based on a finite impulse response (FIR) photonic microwave delay-line filter with nonuniformly-spaced taps. A microwave bandpass differentiator based on a six-tap nonuniformly-spaced photonic microwave delay-line filter with all- positive coefficients is designed, simulated, and experimentally demonstrated. The reconfigurability of the microwave bandpass differentiator is experimentally investigated. The employment of the differentiator to perform differentiation of a bandpass microwave signal is also experimentally demonstrated.

Various properties of linear infinite-dimensional Hamiltonian systems are studied. The structural stability of the Vlasov-Poisson equation linearized around a homogeneous stable equilibrium [mathematical symbol] is investigated in a Banach space setting. It is found that when perturbations of [mathematical symbols] are allowed to live in the space [mathematical symbols], every equilibrium is structurally unstable. When perturbations are restricted to area preserving rearrangements of [mathematical symbol], structural stability exists if and only if there is negative signature in the continuous spectrum. This analogizes Krein's theorem for linear finite-dimensional Hamiltonian systems. The techniques used to prove this theorem are applied to other aspects of the linearized Vlasov-Poisson equation, in particular the energy of discrete modes which are embedded within the continuous spectrum. In the second part, an integral transformation that exactly diagonalizes the Caldeira-Leggett model is presented. The resulting form of the Hamiltonian, derived using canonical transformations, is shown to be identical to that of the linearized Vlasov-Poisson equation. The damping mechanism in the Caldeira-Leggett model is identified with the Landau damping of a plasma. The correspondence between the two systems suggests the presence of an echo effect in the Caldeira-Leggett model. Generalizations of the Caldeira-Leggett model with negative energy are studied and interpreted in the context of Krein's theorem. / text